Mathematical Modeling for Carbon Dioxide Level Within Confined Spaces

Federal regulations require refuge alternatives (RAs) in underground coal mines to provide a life-sustaining environment for miners trapped underground when escape is impossible. A breathable air supply is among those requirements. For built-in-place (BIP) RAs, a borehole air supply (BAS) is commonly used to supply fresh air from the surface. Federal regulations require that such a BAS must supply fresh air at 12.5 cfm or more per person to maintain the oxygen concentration between 18.5% and 23% and carbon dioxide level below the 1% limit specified. However, it is unclear whether 12.5 cfm is indeed needed to maintain this carbon dioxide level. The minimal fresh air flow (FAF) rate needed to maintain the 1% CO₂ level will depend on multiple factors, including the number of people and the volume of the BIP RA. In the past, to predict the interior CO₂ concentration in an occupied RA, 96-h tests were performed using a physical human breathing simulator. However, given the infinite possibility of the combinations (number of people, size of the BIP RA), it would be impractical to fully investigate the range of parameters that can affect the CO₂ concentration using physical tests. In this paper, researchers at the National Institute for Occupational Safety and Health (NIOSH) developed a model that can predict how the %CO₂ in an occupied confined space changes with time given the number of occupants and the FAF rate. The model was then compared to and validated with test data. The benchmarked model can be used to predict the %CO₂ for any number of people and FAF rate without conducting a 96-h test. The methodology used in this model can also be used to estimate other gas levels within a confined space.